Peter was restored:
John 21:15 When they had finished eating, Jesus said to Simon Peter, “Simon son of John, do you love me more than these?”
“Yes, Lord,” he said, “you know that I love you.”
Jesus said, “Feed my lambs.”
John 21:16 Again Jesus said, “Simon son of John, do you love me?”
He answered, “Yes, Lord, you know that I love you.”
Jesus said, “Take care of my sheep.”
John 21:17 The third time he said to him, “Simon son of John, do you love me?”
Peter was hurt because Jesus asked him the third time, “Do you love me?” He said, “Lord, you know all things; you know that I love you.”
Jesus said, “Feed my sheep.
John 21:18 Very truly I tell you, when you were younger you dressed yourself and went where you wanted; but when you are old you will stretch out your hands, and someone else will dress you and lead you where you do not want to go.”
John 21:19 Jesus said this to indicate the kind of death by which Peter would glorify God. Then he said to him, “Follow me!”
I read the Scriptures you posted, but do not see any "restoration". Instead, I see a petty, jealous man, who later found it necessary to try and make Gentiles follow the Jewish customs and could not have been your cult claims as the leader of the church. The head is Christ Jesus, and Peter was only one of 12. The following passage is the completion of your post... and does nothing to reinforce or restore Peter into any role of authority. YMMV, but that is only because of your "traditions of men"!
John 21: ...20 Peter turned and saw that the disciple whom Jesus loved was following them. (This was the one who had leaned back against Jesus at the supper and had said, “Lord, who is going to betray you?”) 21 When Peter saw him, he asked, “Lord, what about him?” p>22 Jesus answered, “If I want him to remain alive until I return, what is that to you? You must follow me.” 23 Because of this, the rumor spread among the believers that this disciple would not die. But Jesus did not say that he would not die; he only said, “If I want him to remain alive until I return, what is that to you?” p>24 This is the disciple who testifies to these things and who wrote them down. We know that his testimony is true.